I went to H&R block and tried to do the online tax preparation, but I can’t get by without his social security number. The problem is that I have no way to get his social. I don’t talk to him anymore and we are in the process of a divorce. Does anyone know a way around this?

No its illegal to file jointly after even a legal seperation much less a divorce.
Sure, file “Married-filing Separately” or if you live alone w/children you can probably file “Head of Household” (providing you qualify)
Did you ever file a joint return with him? If so you should be able to get a transcript from the IRS of that return, and it will have his social security number on it.
See http://www.irs.gov/taxtopics/tc156.html for info on how to request a transcript.
If he is your ex-husband you should be filing as unmarried. There would be no reason to need his social if you are filing a seperate return.
Uh, have you thought about actually maybe speaking to him for a minute and asking?? Swallow your pride, let bygones be bygones and ASK THE MAN.
If you filed jointly in the past, you can contact the IRS and get a tax transcript for free that will have his SSN on it.